It seems that there is no such flight available. From London (United Kingdom) to Melbourne (Australia), both direct flights and connecting flights with transfers at Singapore, Bangkok or Kuala Lumpur are available daily. But these flights are provided by Australia Airlines or Malaysia Airlines. From London(Canada) to Melbourne (Australia), only one connecting flight with two transfers at Vancouver and Inchon is available on every Tuesday.

Of course, the information above is just for your reference, you would better consult the booking agency for more details.